The scientist, 75, said the Virgin boss had offered him a seat.
The physicist and cosmologist, 75, said he had not expected to have the opportunity to experience space but that the Virgin boss had offered him a seat.
Discussing the meaning of happiness on Good Morning Britain, he said: “My three children have brought me great joy.
“And I can tell you what will make me happy, to travel in space.
“I thought no one would take me but Richard Branson has offered me a seat on Virgin Galactic, and I said yes immediately.”
Professor Hawking also shared his views on US President Donald Trump and Labour leader Jeremy Corbyn during the interview.
The scientist – who previously referred to Mr Trump as a “demagogue” – said he still admires America but fears that he “may not be welcome” there any more.
“The reaction to the election of Donald Trump may have been overdone, but it represents a definite swing to a right-wing, more authoritarian approach,” he said.
“Everyday life in the United States continues much the same.
“I have many friends and colleagues there, and it is still a place I like and admire in many ways.
“I would like to visit again and to talk to other scientists but I fear that I may not be welcome.”
Professor Hawking said of Mr Corbyn: “I don’t believe there will be much chance of Labour winning an election under him.
“He doesn’t come across as a strong leader, and he allowed the media to portray him as a left-wing extremist, which he’s not. It’s no good having the right principles if you never get in power.”
But he added: “I will continue to vote Labour, it’s the party that matters.”
Host Piers Morgan also quizzed Professor Hawking about Brexit.
The scientist, who was opposed to leaving the EU, said if the referendum decision must be implemented “it shouldn’t be a hard Brexit as the right wing of the Conservative Party want”.
“That would leave us isolated and inward-looking,” he said. “Instead, we should retain as many links as possible with Europe and the rest of the world, particularly China.”
Professor Hawking also warned that leaving Europe “threatens Britain’s status as a world leader in science and innovation”.